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This is kind of a continuation of this and this previous questions.

  • Say one has a free "classical" field theory which is scale invariant and one develops a perturbative classical solution for an interacting version of that. Then what can be the constraining effects on the perturbation theory from the fact that the free theory was scale invariant? (for an example like this see this recent paper)

  • Can one give a QFT example where this can happen that a non-marginal coupling flows to a non-zero fixed point and the anomalous dimension of the corresponding operator adjusts so that the coupling becomes marginal at that point? (..for the fixed point of the RG flow to be interpreted as a point of scale invariance this adjustment has to happen!..)

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